Final answer:
Raising numbers to a power means multiplying the number by itself a number of times. Non-integer powers involve taking roots and raising to integer powers, while raising expressions inside parentheses involves applying the power to every element within. The operation 4 4√81 x 3 possibly involves taking the fourth root of 81, multiplying by 3, and then raising that result to the power of 4.
Step-by-step explanation:
The mathematical operation in question involves raising numbers to different powers. For example, integer powers indicate that a number is multiplied by itself a certain number of times, such as 4³ being equal to 4 x 4 x 4. When encountering non-integer exponents like 3¹·, we can approach it by taking roots and raising to integer powers, such as taking the tenth-root of 3 and then raising it to the 17th power.
Moreover, in the context of scientific notation, multiplying an exponential term by a number involves adjusting both the coefficient and the exponent, where you can change one and compensate by adjusting the other.
When raising an expression inside parentheses to a power, you apply the power to everything inside. For instance, (2·x³)² would result in raising both the numeral and the variable to the second power.
To simplify the expression (4 4√81 x 3), one would need to calculate the fourth root of 81, then multiply the result by 3, and finally raise the entire expression to the fourth power if that's the intended meaning, which is not clearly stated in the given question but derived from the general context of the provided information.